Transmitters or transceivers convert a digital baseband signal into an analog input signal, which is modulated to produce a radio frequency (RF) signal. The RF signal is amplified by a power amplifier and provided to an antenna for transmission. In most systems, a low-pass filter or reconstruction filter is utilized remove any potential harmonics or images from the analog input signal as a result of the digital-to-analog conversion. The reconstruction filter removes undesirable harmonics in order to prevent them from being amplified by the power amplifier and transmitted in adjacent communication channels, also known as adjacent channel leakage.
In order to keep the analog input signal as pure as possible and minimize distortion, it is desirable that the reconstruction filter have a flat gain response and constant group delay for passband frequencies below the cutoff frequency of the reconstruction filter. However, in order to avoid adjacent channel leakage, the reconstruction filter is generally designed to have a sharp transition and attenuation for frequencies above the cutoff frequency. As a result, in practice, the reconstruction filter is unable to achieve both a flat gain response and constant group delay. Often, the reconstruction filter is tailored for a flat gain response. However, the resulting group delay may lead to undesirable distortion of the analog input signal.
In some systems, an additional filter is utilized to compensate for the group delay of the reconstruction filter, such that the overall group delay of the analog input signal is substantially constant. Generally, this additional filter is realized using one or more second-order active filter topologies as building blocks in a modular fashion. In order to achieve higher quality factors (e.g., quality factors of 10 or more), which in turn allow a system designer to manipulate the group delay, a conventional filter topologies are implemented such that a negative gain component is introduced. As a result, in order to provide a negative gain component without inverting the output signal, these conventional second-order filter topologies are often cascaded or configured in a manner which involves more than one amplifier. For example, a Tow-Thomas biquad circuit utilizes three amplifiers to achieve a high quality factor. Many transmitters are used in mobile devices, such as cellular phones or handheld computers, where the battery life/power consumption and the size of the device are two important design considerations. However, each additional amplifier increases the physical area along with the current and/or power consumption of the filter, and thus, the prior art filter topologies are undesirable.